Strengthening of fully-lamellar TiAl: a dislocation pileup analysis

This paper presents an analysis of the yield stress of the fully lamellar microstructure and its variation with the two length parameters involved, the lamellar thickness and the grain-size. The analysis is made by extending the dislocation pileup model, developed for the explanation of the Hall–Petch relation between the yield stress and the grain-size, to the case of multilayer microstructure with coherent lamellar boundaries. Deformation of the lamellar microstructure is assumed to proceed by dislocations propagating in the formation of a succession of mutually interacting pileups, blocked at the lamellar interfaces and piled-up ultimately against the grain boundary. Numerical calculations of the model show that the propagation of the multiple pileup through the successive layers requires progressive increases in the applied stress, and macroscopic yielding occurs after the dislocation pileup has crossed a large number of layers. For the multilayer `single crystalʹ, the yield stress increases with decreasing lamellar size following the Hall–Petch relationship, until a saturation thickness below which the yield stress is unchanged by lamellar spacing and is equal to the critical stress representing the strength of the interface barrier. In the lamellar polycrystal, the yield stress is predicted to be insensitive to the grain size even if the lamellar interface is many times weaker than the grain boundary.